Question: Solve for $q$, $ \dfrac{4}{q + 2} = \dfrac{q - 7}{5q + 10} + \dfrac{2}{q + 2} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $q + 2$ $5q + 10$ and $q + 2$ The common denominator is $5q + 10$ To get $5q + 10$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ \dfrac{4}{q + 2} \times \dfrac{5}{5} = \dfrac{20}{5q + 10} $ The denominator of the second term is already $5q + 10$ , so we don't need to change it. To get $5q + 10$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ \dfrac{2}{q + 2} \times \dfrac{5}{5} = \dfrac{10}{5q + 10} $ This give us: $ \dfrac{20}{5q + 10} = \dfrac{q - 7}{5q + 10} + \dfrac{10}{5q + 10} $ If we multiply both sides of the equation by $5q + 10$ , we get: $ 20 = q - 7 + 10$ $ 20 = q + 3$ $ 17 = q $ $ q = 17$